Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 1
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 2
“The distribution with the largest
entropy the most consistent with
stated assumptions.”
Not knowing anything, we bet on the flattest distribution.
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 3
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 4
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 5
Binomial
Constraint:
“Expected value
is high”
Poisson
Constraint:
“Expected value
is low”
Exponential
Core function
Same proportional rate
of change across entire
distribution
Gamma
Multiple things have
to happen for the
outcome to transpire
Constraint:
“Events sum up
to form outcome”
Normal
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 6
Do not(!) eye-ball outcome distribution from the histogram of the observed outcomes.
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 7
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 8
Variables interact on outcome scale as a consequence of compression of scale.
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 9
“When a lizard is dead due to
cold temperatures, food
availability won’t matter to it”
Effect of food is conditional on
effect of temperature
This happens even when we
don’t specify an interaction
effect in our model
Finding the slope between an
outcome and a response is tricky
beyond the basic linear regression
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 10
E(y)… Expected
mean value
var(y)… Variance
of outcome
05/03/2021
[Study Group] Bayesian Statistics with the Rethinking Material 11
Link between log-odds
and probability scale we
are interested in as our
outcome
Globe toss example - Probability of water:
The logit link is just one out of many (e.g. probit, log-
log) to be used with binomial distributions.